Questions on the circle, a curve composed of points in a plane that are at a fixed distance from a fixed point.

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3
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2answers
285 views

Calculating position/distance of point on arc of circle

I'm having a hard time trying to wrap my head around this problem. Imagine a line of length $A+B$ with center $C$, with a circle with $d = A+B$ with center at $C$. Now imagine drawing a line at ...
1
vote
2answers
232 views

A question on circle

I was solving sample maths paper and came through this question:- If a ball is dropped on ice having a diameter of 24cm and fill inside with depth of 8cm,find the radius of the circle drawn over ice ...
0
votes
2answers
1k views

formula for finding perimeter of half circle

i was looking for this problem http://www.majortests.com/gre/problem_solving_expl.php?exp=50313039243130243330 and was surprised if it is correct,we know that circumference or perimeter of circle ...
1
vote
1answer
339 views

Euclidean Circle Geometry Problem

Let $\Gamma_1$ and $\Gamma_2$ be two non overlapping circles with centers $O_1$ and $O_2$ respectively. From $O_1$, draw the two tangents to $\Gamma_2$ and let them intersect $\Gamma_1$ at points $A$ ...
5
votes
2answers
312 views

Geometric Identities involving $π^2$

Are there any known geometric identities that have $π^2$ in the formula?
0
votes
1answer
162 views

angle of inscribed triangle

let us consider following problem: we have inscribed triangle,like this we are asked to determine if given $x$ is acute or obtuse,$O$ is center of circle,as i know if $CB$ would be ...
3
votes
1answer
138 views

what does mean swept in lines?

suppose that we have following picture question is which of the following chords are parallel,suppose that all lines are chords and we are checking which of them is parallel 1.$a$ and $f$ ...
4
votes
2answers
615 views

Prove that the centre of the nine-point circle lies on the midpoint of the Euler line

In $\Delta ABC$, $AD, BE, CF$ are the altitudes and $\Delta A'B'C'$ is the medial triangle. $K, L, M$ are the midpoints of $AH, CH, BH$. Consider the nine-point circle with centre $G$ (not to be ...
0
votes
1answer
133 views

Möbius map of two circles to half planes

I am very new to complex analysis and am having some trouble with finding a Möbius map that will take two unit discs to half-planes. I don't have enough reputation to post images, but here is a link ...
0
votes
1answer
923 views

How to calculate the height of a circular segment based on the area.

Given an area of a circular segment, how can one find the height of the circular segment? In the image below, assume the area of the green segment is known. How can one find the value of ...
0
votes
2answers
156 views

A simple circle problem

There is a big circle of radius 20cm and a smaller circle 100 cm away from it of radius 5cm now imagine these two to be 2 tires connected by a chain , where the bigger one completes one rotation how ...
-1
votes
1answer
274 views

Concentric circles of radii 1, 2, 3, …upto 100 are drawn.

Concentric circles radii $1, 2, 3, \ldots , 100$ are drawn. The interior of the smallest circle is colored red and the annular regions are colored alternately green and red, so that no two adjacent ...
0
votes
1answer
4k views

relationship between circumference and revolution

i would like to clarify two things by this problem:first what is relationship between circumference and revolution and also revolution and distant traveled by round object.let us consider following ...
3
votes
4answers
4k views

Is it possible to build a circle with quadratic Bézier curves?

i'm searching for a curve type with a minimum of functionality and maximum of usability. I run into quadratic Bézier curves and i wonder, if its possible to draw a circle with it.
5
votes
1answer
625 views

Can anyone explain intuitively why increasing the circumference by 1 meter always increases the radius by 15.9cm?

I found the mathematical proof, and it is obviously correct. But how can the increase in radius be constant regardless of the starting circumference? With a very small circle, the increase should be ...
3
votes
1answer
127 views

Perimeter of a rectangle with four circles in each corner

my teacher asked a question in exercise for calculate the perimeter of following: I get result of $144\pi$ and some of my friends got $208.2$ as result (assuming $\pi\approx3.14$). Q: what's the ...
0
votes
1answer
114 views

Quadrangle with maximum area in circle

My question is related to my previous one find parameter for maximize area suppose we have $4$ points,with coordinate $A(2\cos t,2\sin t)$ $B(-\cos(2-t), -\sin(2-t))$ $C(-2\cos(t) ,-2\sin(t) )$ ...
0
votes
2answers
190 views

determine position of circle inside square

i need to determine position of circle inside square,let us suppose that we have following picture we have following informations: 1.$ABCD$ is square 2.all small figures ,$KMCE$,$PKEF$,$NPFD$ ...
1
vote
2answers
130 views

Fitting circle into an angle

I've been struggling with this for quite some time now, anyone could help me perhaps with this? Given an angle of an arbitrary degrees, and a circle with radius r. And imagine I would try to push the ...
3
votes
4answers
287 views

Finding the area, general case with angle $\theta$.

Inspired by this question, I am curious to know the more general case. Given the radius of the large circle as $R$ and the angle $\theta \le \pi$, what is the area of the colored section? My ...
2
votes
2answers
450 views

Proof: Invariant angle measure - same result for any circle drawn.

Below I have quoted Wikipedia. I am particular interested in the statement: The value of $\theta$ thus defined is independent of the size of the circle: if the length of the radius is changed ...
7
votes
3answers
384 views

find area of dark part

let us consider following picture we have following informations.we have circular sector,central angle is $90$,and in this sector there is inscribed small circle ,which touches arcs of sectors ...
5
votes
3answers
2k views

Proving the length of a circle's arc is proportional to the size of the angle

How can I prove that: The length of the arc is proportional to the size of the angle. Every book use this fact in explaining radians and the fundamental arc length equation $s = r\theta$. ...
1
vote
1answer
131 views

find area of square part

let us consider following picture where $ABCD$ is square, and using $A$ and $C$ as center,there is drawn arc,we should find area of dark part.we know that length of square is $a$,as i see the ...
0
votes
1answer
172 views

find minimum length of triangle

suppose that we have $ABC$ triangle,with $AB=28$ and $C=120$,we should find minimum length of triangle,if it is know that $AC:BC=3:5$,it is clear that minimum side is $AC$,also because sides are ...
1
vote
2answers
103 views

find angle in triangle

Let us consider problem number 21 in the following link http://www.naec.ge/images/doc/EXAMS/math_2013_ver_1_web.pdf It is from georgian national exam, it is written (ამოცანა 21), where word ...
4
votes
2answers
173 views

A proof in circles.

I need help proving this problem: $AB$ is a diameter of a circle. $CD$ is a chord parallel to $AB$ and $2CD = AB$. The tangent at B meets the line $AC$ produced at $E$. Prove that $ AE = 2AB $. ...
12
votes
4answers
2k views

Is it possible to divide a circle into $7$ equal “pizza slices” (using geometrical methods)?

Or is it possible to divide a circle into n equal "pizza slices" (I don't know how to call these parts, but I think you'll know what I mean), where n hasn't got a common divider with $360$? Or are the ...
1
vote
1answer
242 views

How to prove that a circle passing through the center of the circle of inversion invert to a line?

link to the referenced picture: http://www.flickr.com/photos/90803347@N03/9220374271/ In order to prove the Arbelos Theorem, as in the picture above, one need to prove that the semicircle $C$ invert ...
1
vote
2answers
420 views

Maximum Distance between points on circle

What is the greatest possible distance between two points: one on a circle with radius 1 and centre (1; 2) and the other on a circle with radius 2 and centre (4; 6) I am not familiar with the ...
1
vote
2answers
74 views

Points on a circle

36 points are marked, equally spaced, on the circumference of a circle. Some of the points are marked with crosses in such a way that the distances between every two consecutive crosses are all di ...
0
votes
0answers
138 views

Compute multiple Rectangles area intersect by a circle

I've a need to compute the area of single elements (dice) of a matrix like this: http://i.stack.imgur.com/EKVSz.jpg The matrix is composed by 'c' columns and 'r' rows and every element/rectangle has ...
3
votes
1answer
1k views

Determining the angle degree of an arc in ellipse?

Is it possible to determine the angle in degree of an arc in ellipse by knowing the arc length, ellipse semi-major and semi-minor axis ? If I have an arc length at the first quarter of an ellipse and ...
0
votes
2answers
54 views

Finding a point on a circle

I have a circle that I am trying to find series of points on. I know the radius and horizontal tangent point at the top of the circle. I need to find a point that lies on the circle's circumference ...
1
vote
1answer
52 views

Sectors of a Circle

I am programatically drawing sectors of a circle with radius 55 on a cartesian plane which runs from -55 to 55 on the x and y axes. I would like the first sector to be drawn at 0,55. I know I can ...
0
votes
1answer
85 views

Calculate x,y line terminiating point of section of a circle

I have a Cartesian plane running from -41 to 41 on the x and y axes and a circle centered on 0,0 with a radius of 41 divided up into a number of sections of different areas. I know the percentage ...
4
votes
2answers
353 views

Applonius Circle/ Ford Circle / Infinite GP / Circle Packing

All the smaller circles are mutually tangent and continue to infinity. What is sum of radii of all the smaller circles?
6
votes
3answers
15k views

How to determine the arc length of ellipse?

I want to determine the arc length of a ellipse. So what data should I know ? And what law should I use ? For example I have this ellipse on picture below: How can I determine the $d$ length of ...
1
vote
0answers
91 views

Circle in a simplex

Let $T$ be a $2$-dimensional simplex in $\mathbb{R}^2$. A circle $C(x,y,r) \subset \mathbb{R}^2$ is given by its center $(x,y) \in \mathbb{R}^2$ and radius $r\ge 0$. Show that the set of circles in ...
1
vote
0answers
103 views

Circle Geometry and Conic Section textbook

I seek a textbook for good conic section and circle geometry questions. Slightly above introductory level. - slightly. But I wouldn't mind introductory level questions to consolidate my knowledge. I ...
1
vote
1answer
719 views

How to calculate the inverse of a point with respect to a circle?

The theory said: The inverse of a point $P$, with respect to a circle centered at $O$ and has a radius $r$, is the point $P'$ such that The three points $O$, $P$ and $P'$ are colinear. $OP \times ...
3
votes
1answer
120 views

Find coordinates of intersection between two circles, where one circle is centered on the other

I'm writing a program where an object needs to move from point A to point B. A and B are points on the same circle. Point B corresponds to the intersection between the circle and another circle ...
0
votes
1answer
82 views

Radius of in-circle as a function of the center

I am trying to find the radius of an in-circle in a random triangle as a function of the center of the circle. Let (x,y) in\R^2 be the center of a circle, r the radius then i need an expression of the ...
1
vote
3answers
27 views

If $\overline{OQ}\times\overline{OP}=r^2 $ then $\angle OAP=\frac{\pi}{2}$

I would appreciate if somebody could help me with the following problem Q: if $\overline{OQ}\times\overline{OP}=r^2 $ then $\angle OAP=\frac{\pi}{2}$ ($r$: radius of $C$, $C$: circle, $O$: ...
0
votes
2answers
56 views

Proof Error? A line-segment of a circle is a metric.

In O'searcoid, Metric Spaces, he provides the following example of a metric space: Suppose C is a circle and, for each $a,b ∈ C$, define $d(a,b)$ to be the distance along the line segment from $a$ ...
1
vote
1answer
429 views

Collision between a circle and a rectangle

I am trying to create a simple model for collisions between a circle and a rectangle to be used in a computer game. The reason I am asking this question here rather than stack overflow is that the ...
1
vote
2answers
625 views

What is the area of the shaded region of the square?

To find area of shaded portion in the below figure, the picture generate by following mathematica code. ...
0
votes
1answer
99 views

Tangent of circumscribed circle

I found a solution online which it said : "It's easy noted that $AG.AE$ = $AD^2$ = $AF^2$ (Using tangent of circumscribed circle)" I found this not obvious at all. I know that $AD = AF$ but why it ...
1
vote
2answers
310 views

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral?

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral? I gather it doesn't because most of the proofs I've seen use derivatives etc. If ...
0
votes
1answer
317 views

How to Find the First Moment of Area of a Circular Segment by Integration

Given a segment of circle symmetric about the $y$-axis, I'm wondering how to apply the integral $Q_x = \int y \, dA $ to find the first moment of area with respect to the $x$-axis. I'm having ...